Re: ListDimension function
- To: mathgroup at smc.vnet.net
- Subject: [mg72578] Re: ListDimension function
- From: carlos at colorado.edu
- Date: Thu, 11 Jan 2007 02:28:24 -0500 (EST)
- References: <eo25ue$as5$1@smc.vnet.net>
Many thanks to all of you who sent me solutions by direct email.
For testing purposes I organized them into 7 functions:
ListDim1[v_]:=If[Head[v]===List,1+Max[Map[ListDim1,v],0],0]; (* Don
Taylor *)
ListDim2[lst_]:=Max[Length/@Position[lst,List]]; (* János *)
ListDim3[expr_]:=Max[Length/@Position[{expr},{___}]]; (* David Park *)
ListDim4[l_]:=Depth[DeleteCases[l,_?(!ListQ[#1]&)]]-1; (* Jean-Marc
Gulliet *)
ListDim5[e_]:=Max[Length/@Position[e,List]]; (* Carl Woll *)
ListDim6[list_List]:=Depth[list/.x_List/;(!MemberQ[x,{___}])->{}]-1;ListDim6[_]=0;
(* dh *)
ListDim7[expr_]:=Depth[0*expr]-1; (* Andrzej Kozlowski *)
(I excluded a solution by Adriano Pascoletti, who uses 2 functions)
Here is a quick test:
ListDimTest[e_]:={ListDim1[e],ListDim2[e],ListDim3[e],ListDim4[e],ListDim5[e],
ListDim6[e],ListDim7[e]};
t={1,Null,{},{1,2,3,4},{"s"+1},{{},{},{}}, {Infinity,Indefinite,{}},
{1,{{{{{{x,y*z}}}}}},{6}}, {{{{Sqrt[1+x*y]}}}},
{1,{2,Null+5,3},{{{4,Infinity,-4}}}},
{0,{1,{2,{3^{1,2,3}}}}}, {c*{{1,2},{3+{x,y},4}}} } ;
Print[Table[ListDimTest[t[[i]]],{i,1,Length[t]}]//TableForm];
and the results are
Infinity::indet: Indeterminate expression 0 Infinity encountered.
Infinity::indet: Indeterminate expression 0 Infinity encountered.
0 -Infinity 0 0 -Infinity 0 0
0 -Infinity 0 0 -Infinity 0 0
1 1 1 1 1 1 1
1 1 1 1 1 1 1
1 1 1 1 1 1 1
2 2 2 2 2 2 2
2 2 2 2 2 2 2
7 7 7 8 7 7 7
4 4 4 7 4 4 4
4 4 4 5 4 4 4
5 5 5 5 5 5 5
4 4 4 6 4 4 4
Summary: #1, #3, #6 and #7 returned the correct value across the
board. However #7 produced a warning message when an entry
contained Infinity due to the 0*Infinite operation. It seems that the
most compact solution that works, and produces no messages, is #3.
Congratulations to David.
BTW I found surprising that this is not provided as built-in function,
since it is such a basic operation in list preprocessing.
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